Why is it that all matter in the universe is subject to a spinning
motion? Both at the micro and macro level, bodies spin around their own
axis as well as around other bodies. What is responsible for all this
spinning, and is this maybe the universal force that makes the universe
possible?

David Wiltshire, a physicist at the University of Canterbury, responded.

Spinning is not a universal force, but a general property of particles
moving in response to any force that "conserves angular momentum".

This conservation law holds for any force which acts on two objects with a
strength that depends on intrinsic properties of objects (such as mass or
charge) and on the distance between the two objects, but not on any other
relational quantity such as their relative velocity. Both the two long range
forces of nature, gravity and electromagnetism, have a strength that increases
in proportion to the inverse square of the distance, and so are of this type.
That is why the phenomenon of things spinning is so universal in nature.

If you think of the simple case of the circular motion of a planet
about the Sun, then the force on the planet is always the same strength as its
distance from the Sun does not change. The force always acts in the direction
perpendicular to the instantaneous motion of the planet, no work is being
done. The planet is in a state of perpetual equilibrium characterized by
two physical quantities -- its total energy and angular momentum -- staying the
same. Linear momentum is the product of mass and velocity, where velocity is
the rate of change of distance. For circular motion the magnitude of the
distance is not changing, but the angle in the orbit is continually changing
which is why angular momentum is the relevant concept.

Of course, there can be many motions other than circles - for a planet or
comet in Newtonian mechanics there are ellipses, parabolae and hyperbolae as
well. But all of these orbits have the property that if you were to calculate
the product of the mass, speed and radial distance of the orbiting body from
the Sun then you will always end up with the same number -- the angular
momentum -- which does not change. A comet will speed up as it approaches the
Sun, so that even though the distance to Sun is smaller, the product of the
distance and speed is constant (so long its mass stays the same and is
not evaporated away in a close encounter).

For things that rotate on their axes, the same principle applies. An
ice skater who pirouettes on a frictionless surface will spin faster if
she pulls her arms in, or slower as she moves them out, in such a way that
the product of her component masses, their speeds and distances from the
axis of her rotation stay the same number.

It's a general property of physics that if things can happen, they will
happen. The fundamental forces of nature, including gravity and
electromagnetism, give rise to motions that conserve angular momentum and
total energy. Spinning motions are allowed by such laws; so they are the
things that happen.